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3 years ago

Expand. Your answer should be a polynomial in standard form. (x + 1)(x - 6)

Mathematics

1 answer:

Troyanec [42]3 years ago

7 0

The answer is X^2 - 5x - 6

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Solve the equation 7 minus 2X equals 19

dem82 [27]

Answer: x=-6

Step-by-step explanation:

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3 years ago

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What is the equation of the line that is perpendicular to the given line and passes through point (2,5)?

ad-work [718]

Answer:

$\large\boxed{y=-\dfrac{1}{3}x+1}$

Step-by-step explanation:

$\text{The slope-intercept form of an equation of a line:}\\\\y=mx+b\\\\m-slope\\b-y-intercept\to(0,\ b)$

$\text{Let}\ k:y=m_1x+b_1\ \text{and}\ l:y=m_2x+b_2,\ \text{then}\\\\l\ \parallel\ k\iff m_1=m_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\=======================\\\\\text{We must find the slope of the given line.}\\\\\text{The formula of a slope:}\\\\m=\dfrac{y_2-y_1}{x_2-x_1}\\\\\text{Substitute the coordinates of the given points from the graph (0, 1) and (-3, 2)}\\\\m_1=\dfrac{2-1}{-3-0}=\dfrac{1}{-3}=-\dfrac{1}{3}$

$\text{We have an equation:}\\\\y=-\dfrac{1}{3}x+b\\\\\text{From the coordinates of the point (0, 1) we have the y-intercept:}\ b=1.\\\\\text{Therefore we have the equation:}\\\\y=-\dfrac{1}{3}x+1$

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3 years ago

In ΔJKL, the measure of ∠L=90°, KL = 14 feet, and LJ = 95 feet. Find the measure of ∠K to the nearest degree

Anastaziya [24]

Answer:

Step-by-step explanation:

I honestly don’t know

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3 years ago

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Lim x—> -2 <br> sqrt(3x+10) -2/ x+2

snow_lady [41]

$\displaystyle\lim_{x\to-2}\frac{\sqrt{3x+10}-2}{x+2}$

Rationalize the numerator:

$\dfrac{\sqrt{3x+10}-2}{x+2}\cdot\dfrac{\sqrt{3x+10}+2}{\sqrt{3x+10}+2}=\dfrac{(3x+10)-4}{(x+2)(\sqrt{3x+10}+2)}=\dfrac3{\sqrt{3x+10}+2}$

where the $x+2$ factors in the numerator and denominator cancel. Then the limit is

$\displaystyle\lim_{x\to-2}\frac{\sqrt{3x+10}-2}{x+2}=\lim_{x\to-2}\frac3{\sqrt{3x+10}+2}=\frac3{\sqrt4+2}=\boxed{\frac34}$

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4 years ago

Solve the logarithmic equation. Be sure to reject any value of x that is not in the domain of the original logarithmic expressio

Sidana [21]

9514 1404 393

Answer:

x = 16/3

Step-by-step explanation:

a) The rewritten equation is ...

$\dfrac{x-2}{x+8}=\dfrac{x-1}{x+12}$

b) The solution can be found as ...

$\dfrac{x-2}{x+8}-\dfrac{x-1}{x+12}=0\\\\(x-2)(x+12)-(x+8)(x-1)=0 \qquad\text{numerator of the difference}\\\\(x^2+10x-24)-(x^2+7x-8)=0\\\\3x-16=0\qquad\text{simplified}\\\\x=\dfrac{16}{3}\qquad\text{one solution}$

The solution set is {16/3}.

_____

The applicable rule of logarithms is ...

log(a) -log(b) = log(a/b)

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